Mia and Aubrey started kayaking the Crow Creek River at the same time. Mia started at the top of the river and traveled downstream at a speed of 6 miles per hour. Aubrey started 4 miles farther down the river and traveled downstream at a speed of 3 miles per hour. If they each kept a constant speed, which equation can you use to find h, the number of hours it took for Mia to pass Aubrey? Choices: (A)6h = 3h + 4 (B)6h = 4h + 3 How long did it take for Mia to pass Aubrey? Simplify any fractions. ____ hours

Question

Mia and Aubrey started kayaking the Crow Creek River at the same time. Mia started at the top of the river and traveled downstream at a speed of 6 miles per hour. Aubrey started 4 miles farther down the river and traveled downstream at a speed of 3 miles per hour. If they each kept a constant speed, which equation can you use to find h, the number of hours it took for Mia to pass Aubrey?   Choices: (A)6h = 3h + 4 (B)6h = 4h + 3  How long did it take for Mia to pass Aubrey? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set up equation: Set up the equation to represent the distances traveled by Mia and Aubrey. Mia's distance = Mia's speed * time = 6h Aubrey's distance = Aubrey's speed * time + the head start = 3h + 4 Since Mia started 4 miles behind Aubrey, we want to find the time when Mia's distance equals Aubrey's distance.Write catching up equation: Write the equation that represents the point at which Mia catches up to Aubrey. 6h = 3h + 4 This equation represents the point in time when Mia has traveled the same distance as Aubrey, including Aubrey's 4-mile head start.Solve for time: Solve the equation for h. 6h = 3h + 4 Subtract 3h from both sides to isolate the variable h on one side of the equation. 6h - 3h = 3h + 4 - 3h 3h = 4 Now, divide both sides by 3 to solve for h. h = 4/3Simplify time: Simplify the fraction to find the number of hours it took for Mia to pass Aubrey. h = 4/3 hours This is the time it took for Mia to catch up to and pass Aubrey.

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